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Lower excited electronic states of sulfur (S8): A two-photon study by the thermal lensing method
Volume I5 1, number
CHEMICAL
3
LOWER EXCITED ELECTRONIC STATES OF SULFUR (S,): A TWO-PHOTON STUDY BY THE THERMAL LENSING METHOD R. BINI, P. FOGGI,
I4 October
PHYSICS LETTERS
1988
*
N.Q. LIEM ’ and P.R. SALVI
Laboratorio dl Spettroscopia Molecolare, via G. Capponi 9, 503.2 I Florenre, Italy
Dlpartimento dt Chinuca, Uniwrsit6 di Fircnzc,
Received 20 April 1988; in final form 2 I July 1988
Thermal lensing is applied to the study of multiphoton excitations in sulfur solution and crystal. The polarized two-photon absorption spectrum ofsulfurand the polarization ratio for both the solution and crystal have been measured from 3000 to 2500 A (crystal) and to 2200 a (solution). The results are discussed in terms of electronic energy levels and two-photon absorption tensors of molecular sulfur calculated with semi-empirical methods.
1. Introduction The electronic states of sulfur ( Ss ) have received considerable attention in recent years [ l-61. Charge transport properties of orthorhombic sulfur crystal have been discussed in terms of o and 5cMOs [ 1,2] or, in a more refined model [ 3 1, in terms of orbitals of mixed character. In the iatter case a quantitative estimation of the energy dispersion due to the intermolecular interaction was also given. UV molecular and crystal transitions have been related in most cases [ l-3,5 ] to MO excitation energies, neglecting the interaction between excited configurations. CI of limited extent has been explicitly considered only in one calculation [ 41. It is evident that electronic states other than those that are one-photon active may contribute to the energy spectrum of sulfur and that a knowledge of them could supply a further check for MO calculations. These latter, on the other hand, are of limited interest for spectral assignment unless CI of reasonably large size is taken into account. Experimentally, additional information about excited states is given by two-photon (TP) absorption.
* This work was supported by the Italian Minister0 della Pubblica Istruzionc and Consiglio Nazionale delle Ricerche. ’ On leave from the Institute of Physics of Vietnam, Hanoi, Vietnam.
236
Sulfur represents a particularly interesting case since, assuming for Ss a Ddd symmetry, TP active states belong to A,, Ez and EE3species while one-photon activity is restricted to Bz and E, states. The sulfur molecule is a non-emissive system, therefore induced fluorescence (or phosphorescence) cannot be used as an indirect detection method of multiphoton absorption. Thermal lensing represents a suitable alternative. This technique, which is related to heating effects in the sample following absorption from an exciting beam [7], has been widely used as a spectroscopic probe for oneand multi-photon excitations in gases and liquids in both cw and pulsed experiments [ 81, as suggested by Albrecht and co-workers [ 91. In contrast, reports on thermal lensing in solids are rare. Very recently, a thermal lensing study of the triplet lifetime and formation in pyridazine at low temperature appeared in the literature [ lo]. Here we show that with sufficient care the technique can be extended to determine TP spectra of solids. In this Letter we report on the TP spectrum and polarization ratio of sulfur solution and crystal from 3000 to 2500 8, (crystal) and to 2200 A (solution) at room temperature. The TP data are then analyzed in terms of electronic energy levels and TP absorption tensors of molecular sulfur calculated with MO CI semi-empirical methods. Good agreement be-
0 009-2614/88/$ ( North-Holland
03.50 0 Elsevier Science Publishers Physics Publishing Division )
B.V.
Volume I 5 1, number 3
tween the set of one- and two-photon culations has been obtained.
CHEMICAL
data and cal-
2. Experimental Sulfur (from Carlo Erba. Italy) was recrystallized from chloroform. Freshly prepared 10m2 M solutions in the same solvent were used for the experiment. Oriented pure sulphur monocrystals were kindly supplied by Dr. Perrin (Departement de Recherches Physiques, Paris VI, France). The crystal orientation was checked by measuring the Raman spectrum in all the polarization geometries and comparing it with known data [ 11,121. The experimental apparatus for thermal lcnsing experiments has been described elsewhere [ 131. Briefly, the local variation of refractive index occurring in the sample following the TP absorption from a dye laser is probed with a He-Ne laser. The He-Ne beam divergence will change according to the strength of the TP transition and as a result the light intensity striking the PMT will vary. The quadratic dependence of the signal on the incident energy was carefully checked in all the spectral regions of interest and the normalized signal was obtained with respect to the absolute squared energy of the dye laser. An important condition for a thermal lensing experiment is the good optical quality of the sample. Therefore, special precautions must be taken when working with crystals: bulk defects and surface roughness strongly affect the signal. Sublimation from surfaces of sulfur crystals in air is rapid enough to limit the experiment time to less than one hour. With the sample immersed in water the effect is reduced. Also, when irradiating the crystal with high peak power density (typically more than 20 MW/cm’) we observed sudden changes in the HeNe beam spot quality. Therefore several different combinations of neutral-density filters and focusing lenses were tried. We found that the most intense signal compatible with a reasonably high stability is obtained using 80100 mm focal length lenses and pulse energies around 3-6 uJ. However, because of the inherent scattering from solid samples, we observed large fluctuations of the thermal lensing signal. Generally, while working with low repetition pulsed sources, the noise is reduced by
PHYSICS LETTERS
I4 October
I988
averaging the signal over many laser shots and renormalizing by the squared averaged dye intensity. In our case we increased the spectral S/N ratio by processing thermal lensing data only within a definite range of values and then averaging after a pulscto-pulse renormalization. As a calibration test of our equipment we measured the TP spectrum of naphthalene single crystal in (c*c*) geometry by the thermal lensing method in the 3200-2900 8, wavelength region. Our spectrum compares well with that obtained at room temperature by induced fluorescence [ 14]_
3. Results and discussion Sulfur crystallizes in the orthorhombic system, space group Fddd ( D:z ) with four molecules per unit cell on sites of CZ symmetry [ 1% 17 1. The structure of the free molecule is a puckered octagon of Dd,, symmetry. The correlation between molecular and crystal symmetry and the one- and two-photon selection rules are reported in table 1. 3.1. Solution spectrum The TP absorption spectrum of sulfur solution in linear polarization and the polarization ratio sZ=Ia a/1,, between circular and linear TP intensities in the 3000-2200 A region are shown in fig. 1. As can be seen from table 1, in D,, symmetry onephoton activity is limited to B, and E, species while A,, E, and E, species are TP active in the electric dipole approximation and with the ground state as the initial level. Therefore the TP spectrum is expected to display appreciable differences from the one-photon counterpart. This general prediction is in fact obcycd if WC compare our results with onephoton solution data (see fig. 2). The onset of TP absorption is found around 3000 A. A weak and unstructured absorption occurs across the wavelength region up to 2500 A, in contrast with the one-photon spectrum which has strong absorption bands at 2790 and 2620 A (see fig. 2). The TP spectrum shows only one band around 2430 A, above which the line profile steadily increases with no major absorption maxima. No large variation of the polarization ratio is found (see fig. 1) _i2 values 2 1 are 237
Volume
I5 I, number 3
Table I Correlation
CHEMICAL
diagram of orthorhombic
14 October
PHYSICS LETTERS
sulfur (S,). x, y, z are the molecular axes with zas principal
axis, and a, b, care thecrystal
Molecular
Site
Factor
eymmstry
6ymmc?tty
symmetry
1988
axes
group
Dad
found in all wavelength regions except around the 2430 A band where D decreases to -0.7. As is well known [ 181, D gives information, for randomly oriented samples, on the symmetry of TP transitions. For photons of equal energy, as in our case, sZ< 3 /2 corresponds to totally symmetric transitions and Q=3/2 to non-totally symmetric transitions. However, low-resolution spectra do not very often show the limiting Q= 3/2 value due to overlap
Fig. 1.Normalized two-photon absorption spectrum of a lo-’ M sulfur solution In chloroform in linear polarization (lower trace) and polarization ratio 12 (upper trace) in the 3000-2200 8, spcc-
tral range at room temperature. 238
between bands of different polarization [ 191. Our data clearly show that the 2430 8, band must be assigned to a A, +A, transition. The polarization behaviour in the remaining parl of the spectrum gives less conclusive indications. In fact, considering the general form of the A, TP tensor in table 2, it is easy to derive L?w 1.1 when BZ -A, that is when the zz component is nearly equal and opposite in sign with respect to the XX (or JJ~) tensor component. Alter-
Fig. 2. Comparison of one- (...) and two-photon (-) spectra of sulfur solution in chloroform; t in P mol-’ cm-’ and 6 in arkrrary units.
Volume 151,number 3
CHEMICAL PHYSICS LETTERS
14 October 1988
Table 2 Non-vanishing TP absorption tensors of molecular sulfur ( Ddd symmetry (cq. (1) in section 4)
p(A,)=
I”r.(E,)=(~
-z
a]
A 0 0 0 A 0 ( 0 0 B) w+(;
K i)
natively, we can think of the experimental value .Qz 1 as due to non-totally symmetric TP transitions overlapped with weaker excitations of Al character. In a similar case [ 201, such 52 values have been interpreted as indicative of non-totally symmetric transitions. 3.2. Crystal spectrum The TP absorption spectrum of orthorhombic sulfur in cc geometry at room temperature and the polarization ratio between cc and aa intensities, IJI,,, in the 3000-2500 8, region are shown in fig_ 3. For an excitation wavelength less than 5000 8, (corresponding to an effective TP transition ~2500 A) the thermal lensing signal does not show quadratic dependence on the incident intensity. Below 4800 8, the dependence becomes perfectly linear. This result is confirmed by the one-photon photoacoustic absorption spectrum of sulfur powder (taken on a OAS mode1 400 from EDT Research) whose onset occurs at ~4800 A. The linear dependence for I,,,<4800 8, means that below this value we are thermally probing one-photon crystal transitions. The TP spectrum of crystal sulfur in the 3000-2500 8, region is similar to the solution spectrum. The unstructured intensity profile of sulfur solution splits into two broad bands, one centered at = 2700 A and the other, less defined, around 2900 A. The polarization ratio, &,_/I,,, is equal to or larger than unity with a shallow maximum, = 1.6, around 2750 A, slightly red-shifted with respect to the cc band maximum.
Fig. 3. Normalized two-photon absorption spectrum of sulfur crystal in cc polarization (lower trace) and intensity ratio (I,, /I,, ) (upper trace) in the 3000-2500 8, spectral range at room temperature.
Since crystal field effects do not show clearly in our spectrum, it is more convenient in a first approximation to discuss the results in terms of molecular energy levels and TP tensors, these latter being suitably projected onto crystal axes, and neglecting intermolecular interactions, i.e. using the oriented gas approximation. The molecular TP tensors are corrected in table 2. Then, TP intensities along the crystal axes are proportional to the square of the appropriate crystal tensor elements [21]. The oriented-gas predictions for the sulfur crysta1 are found in table 3. All three molecular tensors, A,, EZ and ES,
Table 3 Proportionality factors for relative TP intensities of sulfur crystal in the oriented-gas approximation ‘)
Xl, A& Af, AL A :<, Ai,
A,
EL
B?
(0.6_4+0.48)’ (0.4A+0.6R)* AZ 0.24(5-A)’ 0 0
0.36EZ 0.1 6E2 El 0.24E2 0.6C2 0.4c2
0.96D2 0.96R2 0 0.04.D~ 0.40* O.hW
=) I,~A:;,I,,~~O.~~A~~+O.~~A~~+A~,,.
239
Volume 151, number 3
CHEMICAL PHYSICS LETTERS
project onto the A, crystal species. However, because of the molecular orientation in the crystal, EJ slates do not contribute to cc TP intensity. Therefore, our cc spectrum is entirely due, in this approximation, to A, and Ez states. E3 symmetry does affect, on the other hand, the polarization ratio I,,./Z,,, by decrcasing this quantity, and in the limiting case of a perfectly isolated E, transition the ratio is zero. E2 states give a value of I,,/I,, equal to N 2.7 independent of the molecular tensor (see tables 2 and 3). Since the experimental ratio is always much smaller than this value we should conclude that also E2 states are absent from our spectrum. However, as we have already pointed out in the last paragraph, the observed ratio can also indicate a mixed polarization behaviour, due to transitions of different symmetry among which those of Ez character contribute more to the TP intensity. TP intensities of A, states depend not only on the molecular orientation in the crystal but also on the values of individual tensor elements (see table 3). The ICC/I,, quantity can assume in this case any value from zero (when B x-A, see table 2 ) to % 2.7 (when A >! B). It is therefore apparent that it is not possible to draw definite conclusions on the states rcsponsible for TP absorption in this region neither from solution nor from crystal data. This emphasizes the importance of MO calculations on sulfur.
4. MO calculations There is no paper dealing with calculation of second-order properties of molecular sulfur. We have therefore performed CNDO/S CI MO calculations of energy levels and TP cross sections in Sg, to have a basis for interpreting OUT TP spectrum. Two types of calculations are possible for sulfur, according to whether we adopt the classic CNDO parameterization for this atom [22] or follow the Clark procedure [ 23 1, first introduced for thiophene, and later extended to the sulfur molecule [ 41. Although with the second choice the photoelectron spectrum of Ss can be fitted quite nicely [ 41, this parameterization is not satisfactory for interpreting the UV spectrum of sulfur solution. In fact, experimentally we observe (see fig. 2; lop4 M solution in chloroform) a doublet around 2700 A and a third stronger band at 2370 240
14 October
I988
A. The doublet structure has been interpreted as due to an E, +A, transition presumably split by the JahnTeller effect [ 5,241. Therefore we expect in the UV region two E, states, corresponding first to the doublet and second to the higher energy band at 2370 A. This spectral pattern cannot be reproduced using the configuration interaction suggested in ref. [4], while on increasing the Cl size the disagreement gets even larger. On the other hand, the CNDO parameterization [22] gave us much better agreement with experiment. A typical result showing energies and oscillator strengths of the first few electronic states calculated with a 49 SEC1 (7 occupied and 7 unoccupied MOs considered) is reported in table 4. The comparison with one-photon data is good: two El states at 2660 A (4.66 eV) and 2210 A (5.25 eV) arc predicted with roughly equal oscillator strength while a third active state of BZ symmetry at 2707 8, (4.58 eV) has vanishingly small intensity. More interesting, a TP state of A, symmetry is calculated at 2540 A (4.88 eV) while other TP-active Ez and E3 states are predicted both below and above the 2A, state. For all these states we have calculated the TP
Table 4 Energies and oscillator strengths of the lowest excited electronic states of molecular sulfur calculated with a 49 SECI. The equilibrium geometry was taken from ref. [ 41 State
E (ev)
1E,
2E, 2E, 2B2
4.40 4.45 4.58 4.66 4.88 5.05 5.13 5.39 5.61 5.25 6.21
Cl.0894 0.008
3E,
6.30
0.085
6.79
0.6196
1E2 lb
6 24 IA, 1% 2E1
Oscillator strength
0.0001 0.0602
_ 4E,
Volume 15 1, number
3
CHEMICAL
PHYSICS LETTERS
14 October
Table 5 Calculated (49 SECI) molecular TP tensor elements (AZ eV- I), relative intensities in linear polarization the five lowest actwe states of molecular sulfur. 6,, ( lAl + 2A, ) has been set equal to I
S and polarization
lb
lb
2‘4,
26
2EZ
4.40 ev
4.45 eV
4.88 eV
5.39 eV
5.61 eV
0.0124 -0.0124
-0.1260 -0.1260 -0.0235
ratio 52 of
0.2413 -0.2413
0.0124
0.2413
-0.0174 -0.0174 0.017
1988
-0.0192 -0.0192
I
0.009
0.02
3.3
0.15
tensors whose form is given in table 2. In a moleculebased reference system and assuming both photons of equal energy, the TP amplitude tensor is defined as [l&l
wP=x,Y,z;P=l,2,
(1)
where, for instance, (g ) CY 1i} is the transition length between the ground (g) and intermediate (i) states of energy vgr and p is the degeneracy index for E2 or Es final states. In a randomly oriented sample, defining &= XJaa&dp&’ and BG= &,~&&~y”d2, the TP intensity in linear polarization is given by
to 2500 8, (see figs. 1 and 3) to lEZ and lE3 states. The observed Sz value in this region, = 1.1, less than the theoretical value for non-totally symmetric transitions, may presumably be ascribed to polarization distortion from overlapping A, vibronic states, given the low contribution to the TP intensity from allowed transitions. A similar conclusion holds also for the crystal spectrum. The polarization ratio maximum, = 1.6, at 2750 8, can then be associated with the IA,+ lEz transition. At energy higher than that corresponding to 2Ai the experimental intensity of the solution spectrum increase agrees well with our prediction of a strongly absorbing 2E2 state. As a consequence the polarization ratio fi increases up to Zl.
1181 6,, =26,+4&G and the polarization
(2) ratio by
Using eqs. ( 1 )- (3 ) we have calculated the TP tensors and intensities of the lowest active states of sulfur starting from the 49 SEC1 data. The results are shown in table 5. The strongest TP bands in linear polarization are respectively 1A, --t 2E2 and 1A, +2A, with intensity ratio 3 : 1. The lowest excited TP transitions, i.e. lA,-+ 1E3 and lA,+lEZ, have much weaker intensities. The calculation correctly predicts the occurrence of an A, state as the first intense TP transition. In addition, the data of table 5 support the assignment of the weak TP absorption region up
5. Conclusions Thermal lensing has been demonstrated to be a reliable spectroscopic technique for probing multiphoton absorption in sulfur solution and crystal. Our study has allowed us to observe the first few TP-active electronic states of sulfur. Strong evidence of a low-lying A, excited state has been given both by experiment and MO calculation. Occurrence of EZ and E3 states is also suggested by our results.
Acknowledgement The authors wish to thank Professor S. Califano for suggesting this research. One of the authors (NQL) wants to thank TWAS Italian Awards Scheme 241
Volume 15 1, number
3
CHEMICAL
PHYSICS
for Research and Training in Italian Laboratories for a grant.
References [l] D.J. Gibbons, Mol. Cryst. Liquid Cryst. 10 (1970) 137. [ 21 BE. Cook and W.E. Spear, J. Phys. Chem. Solids 30 ( 1969) 1125. [3]I.Chen,Phys.Rev.B2(1970) 1053, 1060. [4] W.R. Salaneck, N.O. Lipari, A. Paton, R. Zallen and K.S. Liang,Phys. Rev. B 12 (1975) 1493. [ 51 D.R. Salahub, A.E. Foti and V.H. Smith Jr., J. Am. Chem. sot. 100 (1978) 7847. [ 61A. Datta, J. Mol. Struct. 92 ( 1983) 93. [7] J.P. Gordon, R.C.C. Leite, R.S. Moore, S.P.S. Port0 and J.R. Whinnery, J. Appl. Phys. 36 (1965) 3. [S] D.S. Kliger, Accounts Chem. Rcs. 30 ( 1980) 129. [ 91 R.L. Swofford, M.E. Long and A.C. Albrecht, Science 19 I (1976) 183. [ IO] M. Terazima and T. Azumi, Chcm. Phys. Letters 145 286.
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( 1988)
LETTERS
14 October
1988
[I I] G.A. Ozin, J. Chem. Sot. A (196Y) 116.
[ 121 G. Gautier and M. Debeau, Spectrochim.
Acta 30A ( 1974) 1193. [ 131 P.R. Salvi, P. Fog@, R. BinI and E. Castellucci, Chem. Phys. Letters 141 (1987) 417. [ 141 N. Mikami and M. Ito, Chem. Phys. Letters 3 I ( 1975) 472. [ 151 B.E. Warren and J.T. Burwell, J. Chem. Phys. 3 ( 1935) 6. [ 161 J.C. Abrahams, Acta Cryst. 8 ( 1955) 66 1. [ I 71 A. Caron and J. Donohue, Acta Cryst. 18 ( 1965) 562. [ 181 W.M. McClain and R.A. Harris, in: Excited states, Vol. 3, ed. E.C. Lim (Academic Press, New York. 1978). [ 191 G. Hohlneicherand B. Dick, J. Chem. Phys. 70 ( 1979) 5427. [ 201 B. Dick and G. Hohlneicher, Chem. Phys. Letters 83 ( 1981) 615. [Zl] R.M. Hochstrasser and H.N. Sung, J. Chem. Phys. 66 (1977) 3276. [22] D.P. Santry and G.A. Scgal, J. Chcm. Phys. 47 (167) 15X. [23] D.T. Clark, Tetrahedron 24 (1968) 2263. [24] B. Meyer, T.V. Oommen and D. Jensen, J. Phys. Chem. 75 (1971) 912.
CHEMICAL
3
LOWER EXCITED ELECTRONIC STATES OF SULFUR (S,): A TWO-PHOTON STUDY BY THE THERMAL LENSING METHOD R. BINI, P. FOGGI,
I4 October
PHYSICS LETTERS
1988
*
N.Q. LIEM ’ and P.R. SALVI
Laboratorio dl Spettroscopia Molecolare, via G. Capponi 9, 503.2 I Florenre, Italy
Dlpartimento dt Chinuca, Uniwrsit6 di Fircnzc,
Received 20 April 1988; in final form 2 I July 1988
Thermal lensing is applied to the study of multiphoton excitations in sulfur solution and crystal. The polarized two-photon absorption spectrum ofsulfurand the polarization ratio for both the solution and crystal have been measured from 3000 to 2500 A (crystal) and to 2200 a (solution). The results are discussed in terms of electronic energy levels and two-photon absorption tensors of molecular sulfur calculated with semi-empirical methods.
1. Introduction The electronic states of sulfur ( Ss ) have received considerable attention in recent years [ l-61. Charge transport properties of orthorhombic sulfur crystal have been discussed in terms of o and 5cMOs [ 1,2] or, in a more refined model [ 3 1, in terms of orbitals of mixed character. In the iatter case a quantitative estimation of the energy dispersion due to the intermolecular interaction was also given. UV molecular and crystal transitions have been related in most cases [ l-3,5 ] to MO excitation energies, neglecting the interaction between excited configurations. CI of limited extent has been explicitly considered only in one calculation [ 41. It is evident that electronic states other than those that are one-photon active may contribute to the energy spectrum of sulfur and that a knowledge of them could supply a further check for MO calculations. These latter, on the other hand, are of limited interest for spectral assignment unless CI of reasonably large size is taken into account. Experimentally, additional information about excited states is given by two-photon (TP) absorption.
* This work was supported by the Italian Minister0 della Pubblica Istruzionc and Consiglio Nazionale delle Ricerche. ’ On leave from the Institute of Physics of Vietnam, Hanoi, Vietnam.
236
Sulfur represents a particularly interesting case since, assuming for Ss a Ddd symmetry, TP active states belong to A,, Ez and EE3species while one-photon activity is restricted to Bz and E, states. The sulfur molecule is a non-emissive system, therefore induced fluorescence (or phosphorescence) cannot be used as an indirect detection method of multiphoton absorption. Thermal lensing represents a suitable alternative. This technique, which is related to heating effects in the sample following absorption from an exciting beam [7], has been widely used as a spectroscopic probe for oneand multi-photon excitations in gases and liquids in both cw and pulsed experiments [ 81, as suggested by Albrecht and co-workers [ 91. In contrast, reports on thermal lensing in solids are rare. Very recently, a thermal lensing study of the triplet lifetime and formation in pyridazine at low temperature appeared in the literature [ lo]. Here we show that with sufficient care the technique can be extended to determine TP spectra of solids. In this Letter we report on the TP spectrum and polarization ratio of sulfur solution and crystal from 3000 to 2500 8, (crystal) and to 2200 A (solution) at room temperature. The TP data are then analyzed in terms of electronic energy levels and TP absorption tensors of molecular sulfur calculated with MO CI semi-empirical methods. Good agreement be-
0 009-2614/88/$ ( North-Holland
03.50 0 Elsevier Science Publishers Physics Publishing Division )
B.V.
Volume I 5 1, number 3
tween the set of one- and two-photon culations has been obtained.
CHEMICAL
data and cal-
2. Experimental Sulfur (from Carlo Erba. Italy) was recrystallized from chloroform. Freshly prepared 10m2 M solutions in the same solvent were used for the experiment. Oriented pure sulphur monocrystals were kindly supplied by Dr. Perrin (Departement de Recherches Physiques, Paris VI, France). The crystal orientation was checked by measuring the Raman spectrum in all the polarization geometries and comparing it with known data [ 11,121. The experimental apparatus for thermal lcnsing experiments has been described elsewhere [ 131. Briefly, the local variation of refractive index occurring in the sample following the TP absorption from a dye laser is probed with a He-Ne laser. The He-Ne beam divergence will change according to the strength of the TP transition and as a result the light intensity striking the PMT will vary. The quadratic dependence of the signal on the incident energy was carefully checked in all the spectral regions of interest and the normalized signal was obtained with respect to the absolute squared energy of the dye laser. An important condition for a thermal lensing experiment is the good optical quality of the sample. Therefore, special precautions must be taken when working with crystals: bulk defects and surface roughness strongly affect the signal. Sublimation from surfaces of sulfur crystals in air is rapid enough to limit the experiment time to less than one hour. With the sample immersed in water the effect is reduced. Also, when irradiating the crystal with high peak power density (typically more than 20 MW/cm’) we observed sudden changes in the HeNe beam spot quality. Therefore several different combinations of neutral-density filters and focusing lenses were tried. We found that the most intense signal compatible with a reasonably high stability is obtained using 80100 mm focal length lenses and pulse energies around 3-6 uJ. However, because of the inherent scattering from solid samples, we observed large fluctuations of the thermal lensing signal. Generally, while working with low repetition pulsed sources, the noise is reduced by
PHYSICS LETTERS
I4 October
I988
averaging the signal over many laser shots and renormalizing by the squared averaged dye intensity. In our case we increased the spectral S/N ratio by processing thermal lensing data only within a definite range of values and then averaging after a pulscto-pulse renormalization. As a calibration test of our equipment we measured the TP spectrum of naphthalene single crystal in (c*c*) geometry by the thermal lensing method in the 3200-2900 8, wavelength region. Our spectrum compares well with that obtained at room temperature by induced fluorescence [ 14]_
3. Results and discussion Sulfur crystallizes in the orthorhombic system, space group Fddd ( D:z ) with four molecules per unit cell on sites of CZ symmetry [ 1% 17 1. The structure of the free molecule is a puckered octagon of Dd,, symmetry. The correlation between molecular and crystal symmetry and the one- and two-photon selection rules are reported in table 1. 3.1. Solution spectrum The TP absorption spectrum of sulfur solution in linear polarization and the polarization ratio sZ=Ia a/1,, between circular and linear TP intensities in the 3000-2200 A region are shown in fig. 1. As can be seen from table 1, in D,, symmetry onephoton activity is limited to B, and E, species while A,, E, and E, species are TP active in the electric dipole approximation and with the ground state as the initial level. Therefore the TP spectrum is expected to display appreciable differences from the one-photon counterpart. This general prediction is in fact obcycd if WC compare our results with onephoton solution data (see fig. 2). The onset of TP absorption is found around 3000 A. A weak and unstructured absorption occurs across the wavelength region up to 2500 A, in contrast with the one-photon spectrum which has strong absorption bands at 2790 and 2620 A (see fig. 2). The TP spectrum shows only one band around 2430 A, above which the line profile steadily increases with no major absorption maxima. No large variation of the polarization ratio is found (see fig. 1) _i2 values 2 1 are 237
Volume
I5 I, number 3
Table I Correlation
CHEMICAL
diagram of orthorhombic
14 October
PHYSICS LETTERS
sulfur (S,). x, y, z are the molecular axes with zas principal
axis, and a, b, care thecrystal
Molecular
Site
Factor
eymmstry
6ymmc?tty
symmetry
1988
axes
group
Dad
found in all wavelength regions except around the 2430 A band where D decreases to -0.7. As is well known [ 181, D gives information, for randomly oriented samples, on the symmetry of TP transitions. For photons of equal energy, as in our case, sZ< 3 /2 corresponds to totally symmetric transitions and Q=3/2 to non-totally symmetric transitions. However, low-resolution spectra do not very often show the limiting Q= 3/2 value due to overlap
Fig. 1.Normalized two-photon absorption spectrum of a lo-’ M sulfur solution In chloroform in linear polarization (lower trace) and polarization ratio 12 (upper trace) in the 3000-2200 8, spcc-
tral range at room temperature. 238
between bands of different polarization [ 191. Our data clearly show that the 2430 8, band must be assigned to a A, +A, transition. The polarization behaviour in the remaining parl of the spectrum gives less conclusive indications. In fact, considering the general form of the A, TP tensor in table 2, it is easy to derive L?w 1.1 when BZ -A, that is when the zz component is nearly equal and opposite in sign with respect to the XX (or JJ~) tensor component. Alter-
Fig. 2. Comparison of one- (...) and two-photon (-) spectra of sulfur solution in chloroform; t in P mol-’ cm-’ and 6 in arkrrary units.
Volume 151,number 3
CHEMICAL PHYSICS LETTERS
14 October 1988
Table 2 Non-vanishing TP absorption tensors of molecular sulfur ( Ddd symmetry (cq. (1) in section 4)
p(A,)=
I”r.(E,)=(~
-z
a]
A 0 0 0 A 0 ( 0 0 B) w+(;
K i)
natively, we can think of the experimental value .Qz 1 as due to non-totally symmetric TP transitions overlapped with weaker excitations of Al character. In a similar case [ 201, such 52 values have been interpreted as indicative of non-totally symmetric transitions. 3.2. Crystal spectrum The TP absorption spectrum of orthorhombic sulfur in cc geometry at room temperature and the polarization ratio between cc and aa intensities, IJI,,, in the 3000-2500 8, region are shown in fig_ 3. For an excitation wavelength less than 5000 8, (corresponding to an effective TP transition ~2500 A) the thermal lensing signal does not show quadratic dependence on the incident intensity. Below 4800 8, the dependence becomes perfectly linear. This result is confirmed by the one-photon photoacoustic absorption spectrum of sulfur powder (taken on a OAS mode1 400 from EDT Research) whose onset occurs at ~4800 A. The linear dependence for I,,,<4800 8, means that below this value we are thermally probing one-photon crystal transitions. The TP spectrum of crystal sulfur in the 3000-2500 8, region is similar to the solution spectrum. The unstructured intensity profile of sulfur solution splits into two broad bands, one centered at = 2700 A and the other, less defined, around 2900 A. The polarization ratio, &,_/I,,, is equal to or larger than unity with a shallow maximum, = 1.6, around 2750 A, slightly red-shifted with respect to the cc band maximum.
Fig. 3. Normalized two-photon absorption spectrum of sulfur crystal in cc polarization (lower trace) and intensity ratio (I,, /I,, ) (upper trace) in the 3000-2500 8, spectral range at room temperature.
Since crystal field effects do not show clearly in our spectrum, it is more convenient in a first approximation to discuss the results in terms of molecular energy levels and TP tensors, these latter being suitably projected onto crystal axes, and neglecting intermolecular interactions, i.e. using the oriented gas approximation. The molecular TP tensors are corrected in table 2. Then, TP intensities along the crystal axes are proportional to the square of the appropriate crystal tensor elements [21]. The oriented-gas predictions for the sulfur crysta1 are found in table 3. All three molecular tensors, A,, EZ and ES,
Table 3 Proportionality factors for relative TP intensities of sulfur crystal in the oriented-gas approximation ‘)
Xl, A& Af, AL A :<, Ai,
A,
EL
B?
(0.6_4+0.48)’ (0.4A+0.6R)* AZ 0.24(5-A)’ 0 0
0.36EZ 0.1 6E2 El 0.24E2 0.6C2 0.4c2
0.96D2 0.96R2 0 0.04.D~ 0.40* O.hW
=) I,~A:;,I,,~~O.~~A~~+O.~~A~~+A~,,.
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project onto the A, crystal species. However, because of the molecular orientation in the crystal, EJ slates do not contribute to cc TP intensity. Therefore, our cc spectrum is entirely due, in this approximation, to A, and Ez states. E3 symmetry does affect, on the other hand, the polarization ratio I,,./Z,,, by decrcasing this quantity, and in the limiting case of a perfectly isolated E, transition the ratio is zero. E2 states give a value of I,,/I,, equal to N 2.7 independent of the molecular tensor (see tables 2 and 3). Since the experimental ratio is always much smaller than this value we should conclude that also E2 states are absent from our spectrum. However, as we have already pointed out in the last paragraph, the observed ratio can also indicate a mixed polarization behaviour, due to transitions of different symmetry among which those of Ez character contribute more to the TP intensity. TP intensities of A, states depend not only on the molecular orientation in the crystal but also on the values of individual tensor elements (see table 3). The ICC/I,, quantity can assume in this case any value from zero (when B x-A, see table 2 ) to % 2.7 (when A >! B). It is therefore apparent that it is not possible to draw definite conclusions on the states rcsponsible for TP absorption in this region neither from solution nor from crystal data. This emphasizes the importance of MO calculations on sulfur.
4. MO calculations There is no paper dealing with calculation of second-order properties of molecular sulfur. We have therefore performed CNDO/S CI MO calculations of energy levels and TP cross sections in Sg, to have a basis for interpreting OUT TP spectrum. Two types of calculations are possible for sulfur, according to whether we adopt the classic CNDO parameterization for this atom [22] or follow the Clark procedure [ 23 1, first introduced for thiophene, and later extended to the sulfur molecule [ 41. Although with the second choice the photoelectron spectrum of Ss can be fitted quite nicely [ 41, this parameterization is not satisfactory for interpreting the UV spectrum of sulfur solution. In fact, experimentally we observe (see fig. 2; lop4 M solution in chloroform) a doublet around 2700 A and a third stronger band at 2370 240
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A. The doublet structure has been interpreted as due to an E, +A, transition presumably split by the JahnTeller effect [ 5,241. Therefore we expect in the UV region two E, states, corresponding first to the doublet and second to the higher energy band at 2370 A. This spectral pattern cannot be reproduced using the configuration interaction suggested in ref. [4], while on increasing the Cl size the disagreement gets even larger. On the other hand, the CNDO parameterization [22] gave us much better agreement with experiment. A typical result showing energies and oscillator strengths of the first few electronic states calculated with a 49 SEC1 (7 occupied and 7 unoccupied MOs considered) is reported in table 4. The comparison with one-photon data is good: two El states at 2660 A (4.66 eV) and 2210 A (5.25 eV) arc predicted with roughly equal oscillator strength while a third active state of BZ symmetry at 2707 8, (4.58 eV) has vanishingly small intensity. More interesting, a TP state of A, symmetry is calculated at 2540 A (4.88 eV) while other TP-active Ez and E3 states are predicted both below and above the 2A, state. For all these states we have calculated the TP
Table 4 Energies and oscillator strengths of the lowest excited electronic states of molecular sulfur calculated with a 49 SECI. The equilibrium geometry was taken from ref. [ 41 State
E (ev)
1E,
2E, 2E, 2B2
4.40 4.45 4.58 4.66 4.88 5.05 5.13 5.39 5.61 5.25 6.21
Cl.0894 0.008
3E,
6.30
0.085
6.79
0.6196
1E2 lb
6 24 IA, 1% 2E1
Oscillator strength
0.0001 0.0602
_ 4E,
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Table 5 Calculated (49 SECI) molecular TP tensor elements (AZ eV- I), relative intensities in linear polarization the five lowest actwe states of molecular sulfur. 6,, ( lAl + 2A, ) has been set equal to I
S and polarization
lb
lb
2‘4,
26
2EZ
4.40 ev
4.45 eV
4.88 eV
5.39 eV
5.61 eV
0.0124 -0.0124
-0.1260 -0.1260 -0.0235
ratio 52 of
0.2413 -0.2413
0.0124
0.2413
-0.0174 -0.0174 0.017
1988
-0.0192 -0.0192
I
0.009
0.02
3.3
0.15
tensors whose form is given in table 2. In a moleculebased reference system and assuming both photons of equal energy, the TP amplitude tensor is defined as [l&l
wP=x,Y,z;P=l,2,
(1)
where, for instance, (g ) CY 1i} is the transition length between the ground (g) and intermediate (i) states of energy vgr and p is the degeneracy index for E2 or Es final states. In a randomly oriented sample, defining &= XJaa&dp&’ and BG= &,~&&~y”d2, the TP intensity in linear polarization is given by
to 2500 8, (see figs. 1 and 3) to lEZ and lE3 states. The observed Sz value in this region, = 1.1, less than the theoretical value for non-totally symmetric transitions, may presumably be ascribed to polarization distortion from overlapping A, vibronic states, given the low contribution to the TP intensity from allowed transitions. A similar conclusion holds also for the crystal spectrum. The polarization ratio maximum, = 1.6, at 2750 8, can then be associated with the IA,+ lEz transition. At energy higher than that corresponding to 2Ai the experimental intensity of the solution spectrum increase agrees well with our prediction of a strongly absorbing 2E2 state. As a consequence the polarization ratio fi increases up to Zl.
1181 6,, =26,+4&G and the polarization
(2) ratio by
Using eqs. ( 1 )- (3 ) we have calculated the TP tensors and intensities of the lowest active states of sulfur starting from the 49 SEC1 data. The results are shown in table 5. The strongest TP bands in linear polarization are respectively 1A, --t 2E2 and 1A, +2A, with intensity ratio 3 : 1. The lowest excited TP transitions, i.e. lA,-+ 1E3 and lA,+lEZ, have much weaker intensities. The calculation correctly predicts the occurrence of an A, state as the first intense TP transition. In addition, the data of table 5 support the assignment of the weak TP absorption region up
5. Conclusions Thermal lensing has been demonstrated to be a reliable spectroscopic technique for probing multiphoton absorption in sulfur solution and crystal. Our study has allowed us to observe the first few TP-active electronic states of sulfur. Strong evidence of a low-lying A, excited state has been given both by experiment and MO calculation. Occurrence of EZ and E3 states is also suggested by our results.
Acknowledgement The authors wish to thank Professor S. Califano for suggesting this research. One of the authors (NQL) wants to thank TWAS Italian Awards Scheme 241
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for Research and Training in Italian Laboratories for a grant.
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